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Exactly solvable models of biological invasion

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Author: Petrovskii, Sergei V.; Li, Bai-Lian

Year: 2006

Publisher: Boca Raton, Chapmann & Hall CRC

Series: Chapman & Hall CRC mathematical biology and medicine series

Media group: Ausleihbestand

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Branch: Hauptstelle	Locations: BI-40 173	Status: available	Reservations: 0	Due date:	Barcode: 00178594	Floor plans: Floor plan	Lending note:

Content

Table of Contents

INTRODUCTION

Why exactly solvable models are important

Intra- and inter-species interactions and local population dynamics

Basic mechanisms of species transport

Biological invasion: main facts and constituting examples

MODELS OF BIOLOGICAL INVASION

Diffusion-reaction equations

Integral-difference models

Space-discrete models

Stochastic models

Concluding remarks

BASIC METHODS AND RELEVANT EXAMPLES

The Cole-Hopf transformation and the Burgers equation as a paradigm

Further application of the Cole-Hopf transformation

Method of piecewise linear approximation

Exact solutions of a generalized Fisher equation

More about ansatz

SINGLE-SPECIES MODELS

Impact of advection and migration

Accelerating population waves

The problem of critical aggregation

DENSITY-DEPENDENT DIFFUSION

The Aronson-Newman solution and its generalization

Stratified diffusion and the Allee effect

MODELS OF INTERACTING POPULATIONS

Exact solution for a diffusive predator-prey system

Migration waves in a resource-consumer system

SOME ALTERNATIVE AND COMPLEMENTARY APPROACHES

Wave speed and the eigenvalue problem

Convergence of the initial conditions

Convergence and the paradox of linearization

Application of the comparison principle

ECOLOGICAL EXAMPLES AND APPLICATIONS

Invasion of Japanese beetle in the United States

Mount St. Helens recolonization and the impact of predation

Stratified diffusion and rapid plant invasion

APPENDIX: BASIC BACKGROUND MATHEMATICS

Ordinary differential equations and their solutions

Phase plane and stability analysis

Diffusion equation

References

Index

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Details

Author: Petrovskii, Sergei V.; Li, Bai-Lian

Statement of Responsibility: Sergei V. Petrovskii and Bai-Lian Li

Year: 2006

Publisher: Boca Raton, Chapmann & Hall CRC

Classification: BI-40, BI-50, MA-20

Subject type: Monographien

ISBN: 1584885211

ISBN (2nd): 9781584885214

Description: 217 S. : Ill., graph. Darst.

Series: Chapman & Hall CRC mathematical biology and medicine series

Tags: Ökologie; Biologie Methoden; Biologie; Datenverarbeitung; Mathematik; Biological invasions; Mathematical models; LC; Umwelt

Language: englisch||

Footnote: Literaturangaben

Media group: Ausleihbestand

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